Here's some things you need to consider:
Generally speaking there is often a dive operator on-site at many of the known shore dive entry points. Since they own the land to the water's edge, you're not allowed to bring tanks or gear from off-site locations. This applies at Cobalt Coast and Lighthouse Point - Divetech onsite, Turtle Reef - Sundivers onsite, Eden Rock/Devils Grotto downtown - Eden Rock onsite, and Sunset House south of town.
There's a lot of taller ironshore cliffs in the NW Point area so access to the water is difficult (actually it's the getting out part) in many of what would seem to be shore accessible locations on the map. At Turtle Reef there's a multi-step ladder to the water, CC and LP have a dive dock. View the Cracked Conch (restaurant) website, in their header pictures you can see the cliffs - the ladder shown in one photo is the Turtle Reef access point. Sundivers has a page on their website also.
Depending on which condo complex on NW Point, there is shore access from some properties, from Coconut Bay you can get out to Hepps, from Bonnie's Arch condos - Bonnie's Arch. There's an affiliated dive operator at CB - for Bonnie's Arch you'd have to get gear at Divers Supply as it's a small complex. I've thought about asking the mgmt. whether
non-guests can use the ladder there during the day. They're rented on vrbo.com so it should be possible to contact them. Both would be a decent swim out but mention that it's possible.
The North wall is pretty far out there, at Cobalt Coast they'll tow you out on their dinghy. There's both the mini-wall (great dive) just off Turtle Reef and access to the North Wall farther out. When Divetech was the on-site operator there, they rented scooters to get out to the N. Wall. IDK if Sundivers does now. We've never dove Lighthouse Point but I've read it's a good dive also.
Sometimes there's current off the North side. So what appears to be a shore accessible dive site turns out to be more work than you thought at entry. I've shore dove in San Diego and Maui/Kauai so I have a similar frame of reference to yours.
Theoretically you could shore dive the Kittiwake. You'd have to buy the medallion and surface swim (300 yds?) across an active boat channel (just about every diveop goes out there) though so bring a flag. There's a recent thread about it in this forum.
You're correct about Diver's Supply renting tanks. I believe but am not positive they rent full gear also. They have a Facebook page for contact info. Eden Rock downtown has a 24hr. rental program also - including tanks.
Two accessible shore locations are Cemetery Beach - on the north end of SMB and Smith's Cove south of Sunset House. Bring everything to either. We've wanted to dive Smith's Cove forever just haven't got there yet. It's close to SH so my assumption would be it's similar.
I don't believe (not positive, things change) that there's a dive operator near Kaibo Beach club. The nearest two I'm aware of are Tortuga Divers at Morritt's and Ocean Frontiers in the East End. Tortuga won't let tanks off-site - not sure about OF. I don't think either would rent you gear to remove from their property. I do believe - verify this - that OF would
sell you fills. So you might have to drive all the way to Eden Rock in Georgetown to rent - that has to be over an hour one way. Maybe stop on the drive out from the airport if your flight gets in early enough.
To dive a site like Babylon on the north side requires a longer (15-20min.) surface swim out but is possible. There are several other accessible sites in that area also - a couple near Old Man Bay. McCurley's wall is nearby somewhere. Google it, there's another website with access details - besides
http://shorediving.com/Earth/Caribbean/Cayman_Islands/index.htm
Many of the
boat dive operators that are based farther up Seven Mile Beach - or on the north side - will do North Wall dives due to proximity. Some of the best are Eagle Ray Pass, Ghost Mountain, Babylon. Other good sites off NW Point are Big Tunnel, Orange Canyon, Trinity Caves, the Hepp's sites, etc.
Sunset House is worth a drive down one afternoon, the Mermaid is a classic dive location, My Bar is fun - good food and the Cathy Church Photo School/Gallery is interesting. We thought Eden Rock was very tired, it's walking distance from the cruise port so has gotten a lot of traffic over the decades - others like the Devils Grotto swim-thru's. Go late afternoon when the cruisers are getting ready to leave.
I'm not panning Fosters since they use the same DM/diver ratio as everybody else - 8:1 but you may find up to 24 divers on some of their boats. They're the official cruise operator also. If you're going to stay in the NW Point area, that would be a long drive.
Some of the other dive operators run larger boat "six-pack" operations - check Ambassador Divers, Wall to Wall, Off the Wall, Neptunes, Living the Dream, Indigo etc. for what (for us) would be a better option. Most
won't pick you up in the NW Point area but you could meet them at the marina nearby. If you stay on SMB - Ambassador is based at Comfort Suites. Most include a free shuttle from SMB area hotels/condos.
With a car though it's a non-issue - staying in NW Point you'll definitely want one - things are spaced apart there. And you'll probably drive down to SMB or over to Camana Bay for dinner occasionally. There's a Foster's market in West Bay for food also.
http://www.fosters-iga.com/